css-applied-mathematics2-2013(2)

applied mathematics

Q.No.5.

Q.No.6.

Q.No.7.

Q.No.8.

(10)(a) Workout the Christoffel symbols for the metric tensor g ab a20 0a2sin2

(b) Workout the two dimensional metric tensor for the coordinates p and q given by

(10)

1

p (xy)3

,q 2

x

y

(a) Solve the following system of equations by Jacobi iteration method: (10)

10x + y – 2z = 7.74 x + 12y +3z = 39.66 3x + 4y +15z = 54.8

(b) Solve Sinx = 1 + x3 Using Newton-Raphson method.

(10)(a) Find the root of xex

= 3 by regular falsi method correct to three decimal places.

(10)10

(b)

Evaluate dx

x

2

using (5+5) (10)

01 (i) Trapezoidal rule and (ii) Simpson’s rule.

(a)

Find the real root of the equation Cosx = 3x – 1 correct to seven decimal places (10) by the iterative method.

(b) Use Lagrange’s interpolation formula to find the value of y when x = 10, if the (10)

values

of x and y are given below:

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